Impact of baseline coronary flow and its distribution on fractional flow reserve prediction

1Department of Structural Engineering, Norwegian University of Science and Technology, Trondheim, Norway

2Clinic of Cardiology, St. Olavs Hospital, Trondheim, Norway

3Department of Radiology and Nuclear Medicine, St. Olavs Hospital, Trondheim, Norway

4Department of Circulation and Medical Imaging, Norwegian University of Science and Technology, Trondheim, Norway

Correspondence

Fredrik E. Fossan, Department of Structural Engineering, Norwegian University of Science and Technology, Trondheim, Norway.

Email: fredrik.e.fossan@ntnu.no

Present Address

Frederik E. Fossan, Richard Birkelands, vei 1A,7491 Trondheim, Norway

Abstract

Model‐based prediction of fractional flow reserve (FFR) in the context of stable coronary artery disease (CAD) diagnosis requires a number of modelling assumptions. One of these assumptions is the definition of a baseline coronary flow, ie, total coronary flow at rest prior to the administration of drugs needed to perform invasive measurements. Here we explore the impact of several methods available in the literature to estimate and distribute baseline coronary flow on FFR predictions obtained with a reduced‐order model. We consider 63 patients with suspected stable CAD, for a total of 105 invasive FFR measure-ments. First, we improve a reduced‐order model with respect to previous results and validate its performance versus results obtained with a 3D model.

Next, we assess the impact of a wide range of methods to impose and distribute baseline coronary flow on FFR prediction, which proved to have a significant impact on diagnostic performance. However, none of the proposed methods resulted in a significant improvement of prediction error standard deviation.

Finally, we show that intrinsic uncertainties related to stenosis geometry and the effect of hyperemic inducing drugs have to be addressed in order to improve FFR prediction accuracy.

K E Y W O R D S

coronary flow, fractional flow reserve, reduced‐order model

-This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Abbreviations:CAD, coronary artery disease; CCTA, coronary computed tomography angiography; CO, cardiac output; DBP, diastolic blood pressure; DM, distal murray; FFR, fractional flow reserve; HR, heart rateY age; HU, houndsfield units; ICA, invasive coronary angiography; LAD, left anterior descending; LCX, left circumflex; LM, left main; LVM, left ventricle mass; MAP, mean arterial pressure; PCI, percutaneous coronary intervention; PM, proximal murray; PP, pulse pressure; QCA, quantitative coronary angiography; RCA, right coronary artery; RPDA, right posterior descending artery; SBP, systolic blood pressure; SD, stenosis degree; SV, stroke volume; TAG, transluminal attenuation gradient; TMM, total myocardial mass; US, ultrasound; W, weight.

Int J Numer Meth Biomed Engng. 2019;e3246.

https://doi.org/10.1002/cnm.3246

wileyonlinelibrary.com/journal/cnm 1 of 25

Fractional flow reserve (FFR) is an index to characterise the functional significance of coronary artery stenoses.^1,2 Although FFR is computed as the ratio between invasively measured post‐stenotic and central aortic pressures, this index was originally derived to represent the ratio between the actual transtenotic flow over the hypothetical flow that would be observed in the absence of the stenosis under examination.³The theoretical derivation of FFR assumes con-stant peripheral resistance, which in turn is considered to be achieved under maximal vasodilation.³As a consequence, FFR is measured in hyperemic conditions, normally caused by the administration of a drug, such as adenosine, that selectively vasodilates the coronary peripheral vasculature.⁴A key advantage of FFR over more conventional methods, such as quantitative coronary angiography (QCA), is that, in addition to taking into account the geometry of a given lesion, it implies considering information about flow (under hyperemic conditions). In fact, after having been tested in large trials,^5-7FFR is nowadays recommended to guide revascularization strategy in patients with stable coronary artery disease (CAD) without evidence of ischemia in non‐invasive testing.⁸In practice, if a lesion is below a certain threshold, FFR≤FFRthreshold, with FFRthreshold=0.8, the recommendation is to intervene by performing percutaneous coronary intervention (PCI) or in some instances bypass surgery, while a negative outcome, ie, FFR>FFRthreshold, results in treating the patient with optimal medical therapy.⁸Besides the proven validity of FFR as a a tool for functional assessment of stenosis severity, it remains an invasive procedure with associated risks. Moreover, in a study comprising almost 400 000 patients with suspected CAD from 663 US hospitals, almost two‐thirds of the patients who underwent elective cardiac catheterisation proved to have non‐obstructive CAD as determined by invasive angiography.⁹These considerations have motivated the search for non‐invasive tests to reduce the number of invasive procedures. One of the most promising methods so far is coronary computed tomography angiography (CCTA). CCTA is a non‐invasive anatomical imaging modality that allows to quantify the geometrical significance of a lesion and has a high diagnostic accuracy when compared with invasive coronary angiography‐based diagnosis. A recent randomised trial suggested that CCTA improves patient outcome compared with standard care,¹⁰and guidelines currently suggest considering CCTA as a first‐line test in all patients with suspected stable CAD.¹¹CCTA has shown to be very selective in terms of correctly identifying CAD (FFR≤FFRthreshold), while its performance to exclude CAD (FFR>FFRthreshold) is not as satisfactory, resulting in many false positive recommendations, ie, many patients undergo an invasive procedure for FFR measure-ment that could have been avoided if a more selective non‐invasive method would have been used.¹²

In this scenario, CCTA‐derived FFR has emerged as a possible response to the need for reducing false positive CCTA recommendations. Over the last decade, a significant number of methods for non‐invasive computation of FFR based on CCTA have been proposed.¹³Such methods aim at predicting FFR for a given patient by using non‐invasive information only and have already shown potential to be used as a screening tool on top of CCTA assessment.¹⁴These methods, based on reproducing the fluid mechanics in coronary vessels, share some common general steps that must be followed to deliver FFR predictions: (i) define the computational domain of coronary vessels; (ii) define a mathematical model for fluid mechanics valid in the domain defined in (i); (iii) define boundary conditions; (iv) solve the mathematical model;

and (v) evaluate predicted FFR at desired locations. Although such steps can be found in any model‐based FFR prediction method, the way in which each of these steps is performed varies greatly. In this paper, we address two aspects of this pipeline. First, we consider steps (ii) and (iv), working on the improvement and validation of a reduced‐order model for the coronary circulation that allows for fast and accurate FFR prediction. Then, we focus on step (iii), investigating the impact of several methods for baseline coronary flow estimation and flow distribution proposed so far in the literature on FFR prediction.

Step (ii) of the general modelling strategy defined above requires making a choice on the mathematical model to be used for describing blood flow in coronary arteries. While in principle, many options are available, the most frequent choices found in the literature are 3D incompressible Navier‐Stokes in rigid domains and 1D blood flow models in deformable vessels or fully lumped‐parameter models. In general, 1D or lumped‐parameter models are called reduced‐order models. Several reduced‐order models for FFR prediction have been proposed previously.^15-19However, validation by comparison of predicted FFR with respect to results obtained by using more complex models was under-taken only in.^17-19In Boileau et al,¹⁸a virtual population constructed from a single patient was used, while in Blanco et al,¹⁷a population of 20 patients was considered. Here, we modify the method proposed in Fossan et al¹⁹and validate it on a set of 63 patients (105 FFR measurements). For each patient, we perform simulations using a 3D model for the coronary vessels' domain and use those results as reference. To the best of our knowledge, such an extensive validation of the capacity of a reduced‐order model to reproduce fluid mechanical aspects of model‐based FFR prediction has not been performed so far.

dicted FFR to these boundary conditions was explored in previous studies^19-21and was shown to be extremely relevant.

In particular, Fossan et al¹⁹and Morris et al²¹showed that parameters that determine the hyperemic coronary flow have the highest influence on predicted FFR, for realistic ranges of other parameters. Motivated by this fact, we consider two aspects related to the definition of coronary flow, namely, baseline coronary flow and its distribution among the vessels of the network. In fact, virtually all methods for FFR prediction proposed so far require a baseline flow to be imposed and a criterion to distribute it among vessels in the network. Here, we have selected a set of representative methods for the definition of baseline coronary flow from published works, as well as three alternative methods to distribute such flow among coronary vessels, in order to assess the impact of these modelling choices on FFR prediction. Finally, we perform a sensitivity analysis where we compare the influence of baseline coronary flow to other parameters that are known to be important, namely, the stenosis geometry and the reduction in coronary peripheral resistance from baseline to hyperemic conditions.

The rest of this paper is structured as follows. In Section 2, we describe the acquisition of patient‐specific data (Section 2.1), a reduced‐order model for FFR prediction (Section 2.2), the 3D modelling framework used for validation purposes (Section 2.3), the overall modelling strategy for FFR prediction (Section 2.4), several methods to determine baseline coronary flow (Section 2.5) and its distribution among coronary vessels (Section 2.6), and the method by which a sensitivity analysis of predicted FFR to relevant model parameters was performed (Section 2.7). Section 3 provides a summary of main characteristics of patients involved in the study (Section 3.1), results on the validation of the reduced‐

order model (Section 3.2), and results on the impact of explored modelling strategies on FFR prediction (Section 3.3).

Finally, Section 4 includes a detailed analysis of reported results, as well as considerations on the study limitations and the steps to be taken to (a) improve the reduced‐order model description to better capture the fluid mechanical aspects of the problem under consideration and (b) reduce uncertainty in FFR predictions.

2 | M E T H O D S

2.1 | Patients and data acquisition 2.1.1 | Recruitment

Patients were recruited as part of an ongoing clinical trial at St. Olavs hospital, Trondheim, Norway.²²Patients included in this study had undergone CCTA because of chest pain and suspicion of stable CAD. Patients were enrolled with the findings of at least one coronary stenosis at CCTA examination and were further referred to invasive coronary angiography (ICA) with invasive FFR measurements. Exclusion criteria included nondiagnostic quality of the CCTA, previous percutaneous coronary intervention or bypass surgery, contraindications to adenosine, age (75 years or older), obesity (body mass index greater than 40), and hospitalisation due to unstable CAD after CCTA.

2.1.2 | Medical data acquisition

CCTA

CCTA was performed using 2×128 detector row scanners (Siemens dual source Definition Flash) and 256 detector row CT scanners (Revolution CT, GE Healthcare, Waukesha, Wisconsin, US) with a standardised protocol.²³Left ventricle mass (LVM) was quantified using a commercial software (Syngo.via, Siemens, Germany).

Ultrasound

Echocardiographic imaging was performed using a GE Vivid E95 scanner (GE Vingmed Ultrasound, Horten, Norway).

Cardiac output (CO) was calculated on the basis of the cross‐sectional area of the left ventricle outflow tract (measured immediately proximal to the points of insertion of the aortic leaflets) and velocity time integral derived from PW Doppler.

Fractional flow reserve

FFR was measured using Verrata Plus (Philips Volcano, San Diego, USA) pressure wires according to standard practice.

Intra‐coronary nitroglycerine (0.2 mg) was given to all patients before advancing the pressure wire into the coronary arteries, and hyperemia was induced by continuous intravenous infusion of adenosine at a rate of at least 140μg/kg/

min. Pressure was measured over several cardiac cycles, and FFR measurements were taken during the nadir (lowest

point at the tip of the guiding catheter to ensure that there was no drift. Invasive pressure tracings were recorded and made available for further processing.

Clinical data

Standard non‐invasive diastolic/systolic pressure measurements were performed on both arms as part of clinical routine before ICA using an automatic, digital blood pressure device, Welch Allyn ProBP 3400.

2.2 | Reduced‐order model

Here, we briefly describe the methodology presented in Fossan et al¹⁹for the computation of FFR using a reduced‐order model. FFR predictions obtained with the exact setting proposed in Fossan et al¹⁹will be denoted as FFR_RO^*, while predictions obtained using the improved version of the reduced‐order model introduced in this section will be denoted as FFR_RO*. This is valid throughout the rest of the paper unless otherwise specified.

2.2.1 | Vessels segmentation and computational domain meshing

Segmentation of coronary vessels is performed using the open‐source software ITK‐SNAP.²⁴The output of ITK‐SNAP is a labelled voxel volume identifying segmented vessels and a surface mesh of the segmented volume (in VTK format).

Coronary arteries are segmented until their presence is not distinguishable from surrounding tissue. With this, the resulting average (±standard deviation) outlet radius of coronary arteries included in the computational domain is 0.9±0.23 mm. Surface mesh processing, addition of flow extensions, and 3D meshing are performed using the open‐

source library Vascular Modeling ToolKit (VMTK).^25,26The 3D volume meshes form the basis for both the reference 3D model and the reduced‐order model. For the latter, centerlines are extracted from 3D domains using a centerline extraction algorithm available in VMTK.

2.2.2 | Domain definition

The resulting network of centerlines obtained by the processing steps briefly illustrated in Section 2.2.1 can be concep-tually described as a directed graphG= (V,E), where

• Vare the vertices of the graph, which in this application can represent junctions/bifurcations, a root node, and terminal nodes of the network, hereafter called outlets.

• Eis a set of ordered pairs of vertices, in this case representing vessels.

Graph Gwill have Medges (or vessels) and N vertices. vroot is the vertex at the root of the network, while v^j_out; j¼1; …;Nout, are outlets and v^j_b;j¼0; …;Nb, are vertices representing coupling points among vessels, see Figure 1. Vesselejis described by a set of K^jnodes produced by the centerline extraction algorithm cited in Sec-tion 2.2.1. Each nodek^j_l;l¼1; …;jK^jj, is marked as belonging to a bifurcation region (K^j_b∈K^j), belonging to a ste-nosis (K^j_s∈K^j), or belonging to a 1D domain (K^j_1D∈K^j). The masking of such regions is explained in detail in Fossan et al.¹⁹

Here, we modify the domain definition reported in Fossan et al¹⁹as follows:

• the spacing between nodeskis reduced from 0.5mm to 0.125mm;

• an additional criteria for masking stenotic regions on the basis of the gradient of the radius in the longitudinal direc-tion is added. In Fossan et al,¹⁹a detected stenosis was marked until the estimated stenosis degree (SD) was below 12%. Here, we require that SD > 12%∨jdr

dxj< 0:05. In practice, even though the estimated stenosis degree is below 12%, we continue to mark the region as a stenosis if the location represents a compressiondr

dx< 0:05 or an expansion dr

dx> 0:05.

2.2.3 | Mathematical models

Let us consider a single vesselej. In regions ofejlabelled as 1D domain, ie,K^j_1D∈K^j, blood flow is modelled according to a 1D steady state blood flow model, ie,

∂Q

∂x¼0; (1a)

FIGURE 2 A, Vessels at a bifurcation (graph vertex depicted as a hollow square) with corresponding nodes (circles), nodes masked as belonging to the bifurcation region depicted as filled circles. B, Bifurcation region, nodes are collapsed into one node per vessel (filled circles), at which vessels are coupled using (2b). C, Single vessel with corresponding nodes (circles), nodes masked as belonging to a stenotic region are depicted as filled circles. D, Vessel is split into two vessels, stenosis region nodes collapsed into one node per vessel (filled circles), at which the resulting vessels are coupled using (2b) and (3)

FIGURE 1 Centerline extracted from one subject of the study population. Graph Gstructure is shown with white rectangles representing vertices. In particular, root, outlet vertices, and edges are evidenced.

Edges' regions marked as bifurcation areas are shown in red, stenotic areas are shown in green, and 1D domains are shown in blue. The original 3D segmentation from which centerlines are extracted is shown as a transparent surface

∂

whereA is the cross‐sectional area of the vessel,Qis the blood flow rate, andP is the blood pressure. Moreover, ζ=4.31,¹⁹ρ=1.05g/cm³is the blood density, andμ=0.035 dyne/cm²s is the blood viscosity. The cross‐sectional areaA is assumed constant in time and equal to the area obtained from the segmentation of medical images. Then, the prob-lem unknowns are pressurePand flow rateQ.

Regions masked as bifurcations and stenoses are not modelled using a continuous model. Nodes belonging to such regions are collapsed into a single point, and coupling conditions apply. See Figure 2 for a graphical illustration of this aspect. Coupling for both connection types (bifurcations and stenoses) is performed by enforcing the following relations at the coupling point

whereT is the number of vessels sharing a vertex with the bifurcation/stenosis. For stenoses, we have thatT=2, while in the case of bifurcations, we haveT≥2.ΔPis an additional pressure loss, andλis a coefficient that can assume values between zero and one. At bifurcations,ΔPis set to zero andλis set to one, so that Equation (2a) describes continuity of total pressure. At coupling points representing stenoses, we setλ=0, andΔPis computed as proposed in Seeley and Young,²⁷namely

ΔP¼ Kvμ

whereA0andAsrefer to cross‐sectional areas of the normal and stenotic segments, respectively. Similarly,D0andDs

represent the normal and stenotic diameters. Furthermore, Kv and Kt are empirical coefficients, with Kv¼32 0:83Lð sþ1:64DsÞ·ðA0=AsÞ²=D0,Kt=1.52,²⁷whereasLsis the length of the stenosis.

2.2.4 | Boundary conditions

In this work, we consider two alternative sets of outlet boundary conditions: prescribed flow rate at outlets or resistive elements coupled to outlets. See Section 2.4 for motivation on the two different setups introduced here.

Prescribed flow rates at outlets

Pressure is prescribed at vroot, namely Proot¼^Proot, where P^root is the prescribed pressure. Then, we set Q^j_out¼Q^^j; j¼1; …;Nout, whereQ^^j; j¼1; …;Nout, are the flows to be prescribed deriving from methods described in Sections 2.5 and 2.6. Defining flow rate at outlets implies that flow rate over the entire network is fixed. Then, the only remaining unknown is pressure along 1D domains, and pressure drops over stenotic regions. Such pressure is obtained integrating (1) forQgiven along the 1D domains and evaluating coupling relations (2b) and (3) where appro-priate. A reasonable strategy is to start atvrootand traverse the entire tree, but other choices are possible.

Resistive elements coupled to outlets

As in the previous case, pressure is prescribed atvroot, namelyProot¼P^root. Then, we consider resistive elements coupled to outlets with resistancesR^jout; j¼1; …;Nout. In this case, flow rate is unknown over the entire network, and a non-linear algebraic system has to be solved to find the flow rates at outletsQ^j_out; j¼1; …;Nout, which solve (1), (2b), (3), andProot−P^root¼0. More details on the numerical treatment of the modelling setup strategies presented here are given in Fossan et al.¹⁹

3D simulations are used to validate the reduced‐order model proposed in Fossan et al¹⁹and improved in this work.

These simulations are performed considering segmented coronary trees as rigid domains with a prescribed pressure as inlet boundary condition and either prescribed flows (via prescribed parabolic velocity profile) or lumped‐parameter models attached to each network outlet, according to the modelling pipeline described in Section 2.4. Furthermore, the flow is assumed laminar, and blood is modelled as an incompressible Newtonian fluid. The open‐source library CBCFLOW,²⁸based on FEniCS²⁹is used to solve the resulting mathematical model. The incompressible Navier‐Stokes equations are solved using the incremental pressure correction scheme, described in Simo and Armero.³⁰Tetrahedral elements compose the computational mesh where the velocity field is approximated using piecewise‐quadratic polyno-mials, while linear polynomials are used for pressure. The solver implementation follows very closely the one reported

In document Physics-based and data-driven reduced order models: applications to coronary artery disease diagnostics (sider 87-112)